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• W2045367448 abstract "Let f n denote a kernel density estimator of a bounded continuous density f in the real line. Let Ψ(t) be a positive continuous function such that Under natural smoothness conditions, necessary and sufficient conditions for the sequence scriptstyle{tinR/}big|Psi(t)(fn(t)-Efn(t))big| (properly centered and normalized) to converge in distribution to the double exponential law are obtained. The proof is based on Gaussian approximation and a (new) limit theorem for weighted sup-norms of a stationary Gaussian process. This extends well known results of Bickel and Rosenblatt to the case of weighted sup-norms, with the sup taken over the whole line. In addition, all other possible limit distributions of the above sequence are identified (subject to some regularity assumptions)." @default.
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• W2045367448 date "2004-03-03" @default.
• W2045367448 modified "2023-09-23" @default.
• W2045367448 title "Kernel density estimators: convergence in distribution for weighted sup-norms" @default.
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• W2045367448 doi "https://doi.org/10.1007/s00440-004-0339-x" @default.
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